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Titlebook: Probability Theory; A Comprehensive Cour Achim Klenke Textbook 20081st edition Springer-Verlag London 2008 Probability theory.Random variab

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书目名称Probability Theory
副标题A Comprehensive Cour
编辑Achim Klenke
视频video
概述Comprehensive and modern introduction to the most important fields of probability theory.Unique selection of topics, including many not usually found in introductory texts.Includes supplementary mater
丛书名称Universitext
图书封面Titlebook: Probability Theory; A Comprehensive Cour Achim Klenke Textbook 20081st edition Springer-Verlag London 2008 Probability theory.Random variab
描述.Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as: limit theorems for sums of random variables; martingales; percolation; Markov chains and electrical networks; construction of stochastic processes; Poisson point processes and infinite divisibility; large deviation principles and statistical physics; Brownian motion; and stochastic integral and stochastic differential equations...The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation. .
出版日期Textbook 20081st edition
关键词Probability theory; Random variable; common limit theorems; measure theory; modern probability theory; pr
版次1
doihttps://doi.org/10.1007/978-1-84800-048-3
isbn_ebook978-1-84800-048-3Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag London 2008
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Springer-Verlag London 2008
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Independence,ter the realm of probability theory exactly at this point, where we define independence of events and random variables. Independence is a pivotal notion of probability theory, and the computation of dependencies is one of the theory’s major tasks.
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The Integral,ralises the Lebesgue integral that can be found in textbooks on calculus. Furthermore, the integral is a cornerstone in a systematic theory of probability that allows for the definition and investigation of expected values and higher moments of random variables.
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Moments and Laws of Large Numbers,typical approximate value of the arithmetic mean (. + … + .)/. of i.i.d. random variables (law of large numbers). In Chapter 15, we will see how the variance determines the size of the typical deviations of the arithmetic mean from the expectation.
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Martingales,st lay the foundations for the treatment of general stochastic processes. We then introduce martingales and the discrete stochastic integral. We close with an application to a model from mathematical finance.
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Markov Chains,y of real-world phenomena can be modelled. We give an introduction to the basic concepts and then study certain examples in more detail. The connection with discrete potential theory will be investigated later, in Chapter 19. Some readers might prefer to skip the somewhat technical construction of general Markov processes in Section 17.1.
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